1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 的最简便算法是?越简单越好,计算机算法微积分算法什么的就算了~

1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 的最简便算法是?越简单越好,计算机算法微积分算法什么的就算了~
1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 的最简便算法是?
越简单越好,计算机算法微积分算法什么的就算了~

1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 的最简便算法是?越简单越好,计算机算法微积分算法什么的就算了~
1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10
=1/2+1/12+1/30+1/56+1/90
=(1260+210+84+45+28)/2520
=1627/2520

=1+1/3+1/5+1/7+1/9-1/2-1/4-1/6-1/8-1/10
=1+1/3+1/5+1/7+1/9-1/2(1+1/2+1/3+1/4+1/5)
=1/2(2+2/3+2/5+2/7+2/9)-1/2(1+1/2+1/3+1/4+1/5)
=1/2(1/4+1/3+1/5+2/7+2/9)
=1/6+1/7+1/8+1/9+1/10

1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10
=（1-1/2-1/4-1/8）+（1/3-1/6+1/9）+（1/5-1/10）+1/7
=1/8+5/18+1/5+1/7
=13/40+53/126
=1879/2520